Electrochemical properties of a material are greatly influenced by the behavior of electrons therein. Because the behavior of electrons in a molecule is very complex and difficult to analyze, it cannot be directly evaluated by experiments. In practice, the behavior of an electron is analyzed by computation rather than by experiments, and the concept of a molecular orbital (MO) is used to simulate the behavior of an electron.
Molecular orbitals, which account for the distributions of electrons in a specific region in a molecular structure as a probability concept, cannot be obtained experimentally, but can be constructed using quantum mechanics. Typically, the evaluation of molecular orbitals depends on a qualitative approach in which computed molecular orbitals are depicted as diagrams and visually evaluated. Though useful as a qualitative method to roughly evaluate the entire properties of molecular orbitals, such a method cannot analyze molecular orbitals precisely and objectively. When such a qualitative method is employed, the evaluation of the same molecule may differ from one evaluator to another because the evaluation criterion is absolutely subjective.
In order to surmount problems with such qualitative evaluation methods, the present inventors developed various methods for quantitatively analyzing a molecular orbital by which molecular orbital information can be systematically and precisely evaluated.
For example, there are an infinite number of molecular orbital distribution patterns that may exist in an entire molecular structure. A new block concept was introduced to intuitively and correctively evaluate such complex molecular orbital distribution patterns. A method based on the block concept is designated AC2B (Assembly of Consecutive Building Block).
In the AC2B method, (1) the entire molecular structure of a molecule is divided into blocks, and (2) ratios of molecular orbitals associated with individual blocks to a sum of the entire molecular orbital are calculated, followed by rearranging the blocks consecutively on the basis of the calculated ratios to give a rearranged consecutive block spectrum that accounts for molecular orbital properties. In the rearranged consecutive block spectrum, the first block is responsible for the greatest distribution of the molecular orbital whereas the last block confines the smallest distribution of the molecular orbital. The AC2B method in which advantage is taken of a new block concept can simplify the complex molecular orbital distribution patterns and allows for the precise evaluation of molecular orbital properties in an intuitive manner.
However, the rearranged block spectra created through AC2B intuitively enables the analysis of molecular orbital properties of individual molecules, but cannot be directly applied to the comparison of molecular orbitals between different molecules. This is because the block spectra are consecutive arrangements of blocks according to the ratio size so that they cannot be directly used in quantitative comparison between different molecular orbitals.
The present inventors, therefore, developed a 2BS-score method for determining similarity between different molecular orbitals on the basis of the block spectrum method in which a novel block concept is introduced to precisely express various and complex molecular orbital distribution patterns in an intuitive manner.
The 2BS-score method is designed to quantitatively analyze similarity between two different molecular orbitals by comparing block spectra calculated for the different molecular orbitals. In the 2BS-score method, block spectra of molecular orbitals of interest are compared in a three-step manner to analyze similarity between molecular orbitals. For example, when block spectra of two molecular orbitals to be compared are identical, the 2BS-score is 100%. A larger sequence deviation between block spectra gives a smaller 2BS-score value, which explains poorer similarity between the molecular orbitals. Thus, the 2BS-score method can precisely determine molecular orbital similarity in a quantitative manner.
However, the 2BS-score, although able to quantitatively evaluate molecular orbital similarity, does not provide information on the degree of the similarity deviation. For example, when the two molecular orbital pairs A0-A1 and A2-A3 are evaluated for similarity using 2BS-score, the same 2BS-score values given to the two pairs indicate the same similarity therebetween. In practice, however, similarity between A0-A1 is not identical to that between A2-A3 because there exists a deviation in similarities that A0-A1 and A2-A3 have even at the same 2BS-score values.
Precise measurement of such a similarity deviation would more accurately evaluate similarity between molecular orbitals, and thus could be useful for understanding similarity properties. According to this necessity, the present inventors developed a novel method for statistically evaluating similarity deviation, which is a new property of similarity between molecular orbitals, by quantitatively analyzing similarity between molecular orbitals according to 2BS-score.